عنوان

Algorithmic and Symbolic Combinatorics

(Number (ISBN

9783030670795

Number

E1072

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Algorithmic and Symbolic Combinatorics

General Material Designation

[Electronic book]

Other Title Information

An Invitation to Analytic Combinatorics in Several Variables :

First Statement of Responsibility

/ Stephen Melczer

Place of Publication, Distribution, etc.

Cham

Name of Publisher, Distributor, etc.

: Springer International Publishing

Date of Publication, Distribution, etc.

, 2021

Specific Material Designation and Extent of Item

1 online ressource (XVIII, 418 p. 45 illus., 36 illus. in color)

Series Title

Texts and Monographs in Symbolic Computation Series

Text of Note

Intro -- Foreword -- Preface -- Contents -- List of Symbols -- Chapter 1 Introduction -- 1.1 Algorithmic Combinatorics -- 1.1.1 Analytic Methods for Asymptotics -- 1.1.2 Lattice Path Enumeration -- 1.2 Diagonals and Analytic Combinatorics in Several Variables -- 1.2.1 The Basics of Analytic Combinatorics in Several Variables -- 1.2.2 A History of Analytic Combinatorics in Several Variables -- 1.3 Organization -- References -- Part I Background and Motivation -- Chapter 2 Generating Functions and Analytic Combinatorics -- 2.1 Analytic Combinatorics in One Variable2.1.1 AWorked Example: Alternating Permutations -- 2.1.2 The Principles of Analytic Combinatorics -- 2.1.3 The Practice of Analytic Combinatorics -- 2.2 Rational Power Series -- 2.3 Algebraic Power Series -- 2.4 D-Finite Power Series -- 2.4.1 An Open Connection Problem -- 2.5 D-Algebraic Power Series -- Appendix on Complex Analysis -- Problems -- References -- Chapter 3 Multivariate Series and Diagonals -- 3.1 Complex Analysis in Several Variables -- 3.1.1 Singular Sets of Multivariate Functions -- 3.1.2 Domains of Convergence for Multivariate Power Series -- 3.2 Diagonals3.2.1 Properties of Diagonals -- 3.2.2 Representing Series Using Diagonals -- 3.3 Multivariate Laurent Expansions and Other Series Operators -- 3.3.1 Convergent Laurent Series and Amoebas -- 3.3.2 Diagonals and Non-Negative Extractions of Laurent Series -- 3.4 Sources of Rational Diagonals -- 3.4.1 Binomial Sums -- 3.4.2 Irrational Tilings -- 3.4.3 Period Integrals -- 3.4.4 Kronecker Coefficients -- 3.4.5 Positivity Results and Special Functions -- 3.4.6 The Ising Model and Algebraic Diagonals -- 3.4.7 Other Sources of Examples -- Problems -- ReferencesChapter 4 Lattice Path Enumeration, the Kernel Method, and Diagonals -- 4.1 Walks in Cones and The Kernel Method -- 4.1.1 Unrestricted Walks -- 4.1.2 A Deeper Kernel Analysis: One-Dimensional Excursions -- 4.1.3 Walks in a Half-Space -- 4.1.4 Walks in the Quarter-plane -- 4.1.5 OrthantWalks Whose Step Sets Have Symmetries -- 4.2 Historical Perspective -- 4.2.1 The Kernel Method -- 4.2.2 Recent History of Lattice Paths in Orthants -- Problems -- References -- Part II Smooth ACSV and Applications -- Chapter 5 The Theory of ACSV for Smooth Points -- 5.1 Central Binomial Coefficient Asymptotics5.1.1 Asymptotics in General Directions -- 5.1.2 Asymptotics of Laurent Coefficients -- 5.2 The Theory of Smooth ACSV -- 5.3 The Practice of Smooth ACSV -- 5.3.1 Existence of Minimal Critical Points -- 5.3.2 Dealing with Minimal Points that are not Critical -- 5.3.3 Perturbations of Direction and a Central Limit Theorem -- 5.3.4 Genericity of Assumptions -- Problems -- References -- Chapter 6 Application: Lattice Walks and Smooth ACSV -- 6.1 Asymptotics of Highly Symmetric Orthant Walks -- 6.1.1 Asymptotics for All Walks in an Orthant -- 6.1.2 Asymptotics for Boundary Returns

0

Entry Element

Logic, Symbolic and mathematical

Entry Element

Discrete mathematics

Entry Element

Algorithms

a05

Class number

Entry Element

Melczer, Stephen

Country

ایران

Agency

032

Date of Transaction

20211229

Date and Hour of Consultation and Access

UT_SCI_BL_DB_1000008_0001.pdf

e

BL

278840

1

Y